Simplify the following expression: $ x = \dfrac{1}{9} - \dfrac{a - 1}{a - 7} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{a - 7}{a - 7}$ $ \dfrac{1}{9} \times \dfrac{a - 7}{a - 7} = \dfrac{a - 7}{9a - 63} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{a - 1}{a - 7} \times \dfrac{9}{9} = \dfrac{9a - 9}{9a - 63} $ Therefore $ x = \dfrac{a - 7}{9a - 63} - \dfrac{9a - 9}{9a - 63} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{a - 7 - (9a - 9) }{9a - 63} $ Distribute the negative sign: $x = \dfrac{a - 7 - 9a + 9}{9a - 63}$ $x = \dfrac{-8a + 2}{9a - 63}$